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20 Mar 2019, 04:43
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
50% (02:18) correct
50%
(02:32)
wrong
based on 210
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x and y satisfy the equation x^2 + y^2 = 10x - 6y - 34. What is x + y?
(A) 1
(B) 2
(C) 3
(D) 6
(E) 8
(A) 1
(B) 2
(C) 3
(D) 6
(E) 8
20 Mar 2019, 04:58
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Use concept of (a+b)² on both x and y. Split 34 into 25 and 9
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20 Mar 2019, 05:19
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Bunuel
The equation \(x^2 + y^2 = 10x - 6y - 34\) can be re-written as \(x^2 - 2(5)x + (5)^2 + y^2 + 2(3)y + (3)^2 = 0\)
-> \((x - 5)^2 + (y + 3)^2 = 0\) based on formulae \((a + b)^2 = a^2 + 2ab + b^2\) and \((a - b)^2 = a^2 - 2ab + b^2\)
Therefore, for equation to be equal to zero, x = 5 and y = -3 and the value of x + y = 2(Option B)
